How to get Property Panel attached My Panel?
Reuse the code.

Can turn on developer extras and view the source of most of blenders UI.
An option would be to copy the code needed and add to a new Panel class.
A rub is the properties area often has context members unique to the region. For this  case  context.particle_system is defined in the properties area in particles tab.
Would instead need to be edited to context.object.particle_systems.active
Monkey patching and passing context object with extra members.
As an example have given new panel a method which refers to blenders UI class draw method.  A namespace object is used to create a context with the extra members and passed to the draw method as a proxy context object.
Similarly with  the poll method of the PARTICLE_PT_render_collection class.
Could do same for  draw_header
Have, however,  simply added the use count property to the draw method, it could however be used in a draw header method to replace &quot;Hello World&quot; title.
import bpy
from argparse import Namespace

from bl_ui.properties_particle import (
         PARTICLE_PT_render_collection_use_count,
         PARTICLE_PT_render_collection)
         

class HelloWorldPanel(bpy.types.Panel):
    &quot;&quot;&quot;Creates a Panel in the Object properties window&quot;&quot;&quot;
    bl_label = &quot;Hello World Panel&quot;
    bl_idname = &quot;OBJECT_PT_hello&quot;
    bl_space_type = 'VIEW_3D'
    bl_region_type = 'UI'

    @classmethod
    def poll(cls, context):
        ps = context.object.particle_systems.active
        c = Namespace(**context.copy())
        c.particle_system = ps
        return PARTICLE_PT_render_collection.poll(c) 
    # monkey       
    draw_part = PARTICLE_PT_render_collection_use_count.draw
    
    def draw(self, context):
        layout = self.layout
        ps = context.object.particle_systems.active
        if ps:
            layout.prop(ps.settings, &quot;use_collection_count&quot;)
            c = Namespace(**context.copy())
            c.particle_system = ps
            self.draw_part(c)


def register():
    # fake a pin_id for 3d view.
    bpy.types.SpaceView3D.pin_id = None
    bpy.utils.register_class(HelloWorldPanel)


def unregister():
    del bpy.types.SpaceView3D.pin_id
    bpy.utils.unregister_class(HelloWorldPanel)


if __name__ == &quot;__main__&quot;:
    register()

Note, this is only a proof of concept.  Other things to consider when moving from properties area elsewhere is context.space.pin_id for when the panel is pinned.  Have added another monkey patch to set pin in 3d view to none.